Ground state connectivity of local Hamiltonians Speaker(s): Jamie Sikora
Abstract:
The study of ground spaces of local Hamiltonians is a fundamental task in condensed matter physics. In terms of computational complexity theory, a common focus in this area has been to estimate a given Hamiltonian’s ground state energy. However, from a physics perspective, it is sometimes more relevant to understand the structure of the ground space itself. In this talk, we pursue the latter direction by introducing the notion of “ground state connectivity” of local Hamiltonians. In particular, we show that determining how “connected” the ground space of a local Hamiltonian is can range from QCMAcomplete to NEXPcomplete. (Here, QCMA is the same as QMA, but with a classical witness.) As a result, we obtain a natural QCMAcomplete problem, a task which has generally proven difficult since the conception of QCMA over a decade ago. Date: 01/12/2014  4:00 pm
